What are the multiple pads for in this capacitor?
Is it just to minimize inductance in the solder joints by having four of them on each side? Is it a package with multiple capacitors in it? How should it be applied? I looked at the datasheet, but I still don't know.

Because the silicon chip is large, and a cap on one side could only be connected to the other side of the chip by thin traces within the silicon. So the little doodads on the other side of the silicon get poor capacitizing.

If you put caps on both sides (or all 4 sides) of the silicon chip the caps are closer to all the little doodads on the chip.